A circle with the radius of 2.2 centimetres is drawn touching the sides of a square. What area of the square is NOT covered by the circle?

Does This Sound about Right?

Stage: 3 Challenge Level:

Why do this problem ?

This problem gives practice with the use of estimating numbers and deciding whether an estimated answer is reasonable. These are crucial mathematical skills in the sciences. These interesting questions will allow students to practise these skills whilst developing awareness of orders of magnitude in scientific contexts. As with any problems involving
approximation, they offer opportunity for classroom discussion and justification.

Possible approach

There are several parts to this question, arranged in approximate order of difficulty. The individual pieces could be used as starters or filler activities for students who finish classwork early. Enthusiastic students might work through them in their own time. If students disagree with each other, or with the answers provided, this could lead to productive discussion.

Key questions

Do you have all the information you need to check the calculation? If not, where can you find out what you need?
What formulae will you need to use?
How accurate do you think the answer is?
What 'order of magnitude' checks could you make to test that your answer is sensible?

Possible extension

Can students make up similar questions? Can they put any upper or lower bounds on the actual numbers that would arise from a detailed calculation?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.